This invention relates to the determination of mass flow rate and, more particularly, to an accurate, non-iterative method of calculating mass flow rate using a pressure differential device, such as a venturi flow meter. In an exemplary application, this non-iterative method can be implemented within the controller of a combined-cycle power generation system for computing steam flow rate for each venturi in the steam cooling system.
The steam cooling system for a combined cycle plant incorporates multiple venturis for steam flow rate control and protection. These venturis must provide accurate flow rate information over a range of steam pressures and temperatures to ensure successful operation of the system.
With reference to FIG. 1, a venturi 10 is a pressure differential device which is inserted in a conduit and is used to determine the rate of flowing fluid within the conduit. In FIG. 1 a conduit 12 is illustrated having a longitudinal flow path through which a fluid may flow as shown by the flow arrow. The upstream pressure P1 is sensed by a fluid pressure sensor 14. A temperature probe 16 is provided to detect fluid temperature upstream. Pressure P2 is detected in the throat 18 of the venturi. A flow computer or processor 20 receives pressure P1, pressure P2 and the temperature T. Based on this information and predetermined information, the processor calculates the flow rate. The measurements are shown referenced to upstream conditions only as an example.
Discharge coefficient is a variable in the computation of venturi mass flow rate. Reynolds number is a measure of the ratio of the inertial to viscous forces that the flowing fluid experiences within the venturi. A flow calibration performed on the venturi will reveal how the discharge coefficient varies with Reynolds number. A typical plot of flow calibration data is illustrated in FIG. 2. Note that the discharge coefficient drops off quite rapidly for low Reynolds numbers.
The current approach to obtaining venturi mass flow rate involves either an iteration upon mass flow rate or an assumption of constant discharge coefficient.
In accordance with the iteration method, since both discharge coefficient and Reynolds number are a function of mass flow rate, which is unknown, a guess is first made at the discharge coefficient. From this discharge coefficient, a mass flow rate, qm, is computed as follows, using the ASME definition of venturi mass flow rate, See e.g., xe2x80x9cMeasurement of Fluid Flow in Pipes Using Orifice, Nozzle, and Venturi,xe2x80x9d ASME MFC-3M-1989:
qm=0.09970190CY1d2(hwxcfx81fl/(1xe2x88x92xcex24))0.5xe2x80x83xe2x80x83(1)
wherein:
qm=mass rate of flow, lbm/sec
C=venturi discharge coefficient, dimensionless
Y1=expansion factor based on upstream absolute static pressure, dimensionless
d=venturi throat diameter at flowing conditions, inch
D=upstream internal pipe diameter at flowing conditions, inch
hw=differential pressure, inches of water
xcfx81fl=density of the flowing fluid based on upstream absolute static conditions, lbm/cuft
xcex2=diameter ratio at flowing conditions, xcex2=d/D, dimensionless
Reynolds number, Rd is then computed from mass flow rate as follows:
Rd=48qm/(xcfx80dxcexc)xe2x80x83xe2x80x83(2)
wherein:
Rd=Reynolds number referred to d, dimensionless
qm=mass rate of flow, lbm/sec
d=venturi throat diameter at flowing conditions, inch
xcexc=absolute viscosity of the flowing fluid, lbm/ft-sec, based on upstream temperature.
In the same reference (ASME MFC-3M-1989), an equivalent expression for mass flow rate based on downstream conditions (pressure and temperature) is given.
Since the venturi flow calibration is typically presented as a curve relating discharge coefficient to Reynolds number (see, for example, the typical calibration curve of FIG. 2), a new discharge coefficient can then be computed from the Reynolds number. From this new discharge coefficient, a new mass flow rate is then computed using Equation 1. This process is repeated until the change in computed mass flow rate from one iteration to the next is insignificant.
In accordance with the constant discharge coefficient method, discharge coefficient is assumed to be constant, which eliminates the need to iterate. However, this method limits the ability to accurately compute mass flow rate, especially in the low Reynolds number region where the discharge coefficient can vary quite dramatically.
A non-iterative method for obtaining mass flow rate using a pressure differential flow meter is provided by the invention. More specifically, a non-iterative routine has been developed to compute mass flow rate quickly and accurately by incorporating the results from a flow calibration performed on each venturi directly in the computation.
Accordingly, the invention is embodied in a method for determining mass flow rate of a fluid flowing through a conduit having a first flow passage area, comprising the steps of: providing a pressure differential device comprising a flow constriction defining a fluid passage having a second flow passage area; flowing fluid through the pressure differential device; sensing a fluid pressure P1 at a first pressure sensing location in the conduit remote from the flow constriction; sensing a fluid pressure P2 at a second pressure sensing location downstream of an entrance of the flow constriction; and determining the mass flow rate based on sensed values of the fluid pressure P1 and the fluid pressure P2, and an expression of discharge coefficient C as a function of Reynolds Number Rd determined from flow calibration data obtained by performing a flow calibration on the flow constricting member. In the presently preferred embodiment, the functional expression is a polynomial expression, and the mass flow rate is determined based on the polynomial coefficients of the polynomial expression. In the presently preferred embodiment, furthermore, a fluid temperature T in the conduit is also sensed and the sensed temperature is used in the determination of mass flow rate.